Blue phosphorene is an interesting two-dimensional material, which has attracted the attention of researchers, due to its affluent physical and chemical properties. In recent years, it was discovered that the intercalation of alkali metals and alkaline earth metals in two-dimensional materials may lead to conventional BCS superconductivity. In this work, the electronic structure, phonon dispersion, Eliashberg spectral function, electron-phonon coupling, and the critical temperature of blue phosphorene bilayer intercalated by alkali metals (Li, and K) and alkaline earth metals (Ca, and Sr) for both AB and AC stacking orders are studied using the density functional theory and the density functional perturbation theory, within the generalized gradient approximation with van der Waals correction. The present work shows that the blue phosphorene bilayer is dynamically stable in AB stacking for Li and AC stacking for K, Ca, and Sr, and after intercalation, it transforms from a semiconductor to a metal owing to charge transfer between intercalated atoms and phosphorene. Furthermore, the electron-phonon coupling constant and the critical temperature are higher than those of two-dimensional BCS-type superconductors. They are about 3 and 24.61 K respectively for K-intercalated blue phosphorene bilayer. Thus, our results suggest that blue phosphorene is a good candidate for a superconductor.